Classical simulation of boson sampling based on graph structure

TL;DR

This paper introduces classical algorithms leveraging graph structure to simulate boson sampling efficiently, revealing a sharp transition in complexity related to circuit depth and demonstrating practical advantages over experimental data.

Contribution

The work presents novel graph-structure-based classical algorithms for boson sampling, analyzing their complexity and transition points, and benchmarking against real experiments.

Findings

Efficient simulation possible when circuit depth is less than quadratic in lattice spacing.

Complexity sharply transitions from sub-exponential to exponential as photons interfere more.

Treewidth-based algorithm outperforms experimental likelihood in recent Gaussian boson sampling data.

Abstract

Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum supremacy using noisy intermediate-scale quantum devices. In this work, we present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. The algorithms' complexity grows as so-called treewidth, which is closely related to the connectivity of a given linear-optical circuit. Using the algorithms, we study approximated simulations for local Haar-random linear-optical circuits. For equally spaced initial sources, we show that when the circuit depth is less than the quadratic in the lattice spacing, the efficient simulation is possible with an exponentially small error. Notably, right after this depth, photons start to interfere each other and the algorithms' complexity becomes sub-exponential in the number of sources, implying that there is a sharp transition of its complexity. Finally, when a circuit is sufficiently deep enough for photons to typically propagate to all modes, the complexity becomes exponential as generic sampling algorithms. We numerically implement a likelihood test with a recent Gaussian boson sampling experiment and show that the treewidth-based algorithm with a limited treewidth renders a larger likelihood than the experimental data.